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Name 3-1 Date Solve. Write a multiplication equation for each problem. Miguel swam 6 lengths of the pool. Po Lan swam 3 times as far 1 as far as Miguel. as Miguel. Lionel swam __ 3 1. How many lengths did Po Lan swim? Write the equation. 2. How many lengths did Lionel swim? Write the equation. Chris cut a length of rope that was 12 feet long. Dayna cut a rope 4 times as long as Chris’s rope. Benita cut a rope 1 __ as long as Chris’s rope. 4 3. How long is Dayna’s rope? Write the equation. 4. How long is Benita’s rope? Write the equation. Write two statements for each pair of treats. Use the word times. 5. Compare cookies and drinks. © Houghton Mifflin Harcourt Publishing Company Treat Number 24 6. Compare drinks and pizzas. 8 7. Compare cookies and pizzas. 2 Solve. 1 ⋅ 18 = 8. __ 3 1 11. __ of 27 = 9 UNIT 3 LESSON 1 1 of 12 = 9. __ 4 1 12. __ ⋅ 56 = 8 1 10. __ ⋅ 32 = 8 1 13. __ of 15 = 3 Basic Multiplication Concepts 47 Name 3-1 Date Use the number lines to complete Exercises 1–3. Thirds 0 3 1 3 2 3 3 3 Sixths 0 6 1 6 2 6 3 6 4 6 5 6 6 6 Twelfths 0 1 2 3 4 5 6 7 8 9 10 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 2 1. If you run __ mile, how many sixths have you run? 3 5 2. If you measure __ meter, how many twelfths have you measured? 6 8 3. If you have ___ of a pizza, how many thirds do you have? 12 Write each fraction as a decimal. 76 = 4. _____ 1,000 7 = 5. ___ 10 49 = 6. ____ 32 = 7. _____ 100 1,000 8. 0.28 + 0.43 = 9. 0.7 + 0.04 = 10. 7.8 - 1.95 = 1 times 30 equals 6. 11. Stretch Your Thinking Draw a diagram that shows __ 5 48 UNIT 3 LESSON 1 Basic Multiplication Concepts © Houghton Mifflin Harcourt Publishing Company Add or subtract. 3-2 Name Date Multiply. 2 ⋅ 15 = 1. __ 3 2. __ ⋅8= 7 3. __ ⋅ 32 = 2 4. __ ⋅ 27 = 3 5. __ ⋅ 56 = 3 6. __ ⋅ 16 = 2 7. __ ⋅ 21 = 4 8. __ ⋅ 35 = 5 9. __ ⋅ 28 = 4 10. __ ⋅ 45 = 5 ⋅ 11. ___ 24 = 9 ⋅ 12. ___ 70 = 7 13. __ ⋅ 18 = 5 14. __ ⋅ 80 = 4 15. ___ ⋅ 45 = 3 9 3 9 9 4 8 4 8 5 7 12 10 15 8 Show your work. Solve. 16. Rebecca has 21 math problems to solve. She has solved 2 __ of them. How many problems has she solved? © Houghton Mifflin Harcourt Publishing Company 7 17. Tessa shot 36 free throws. She made 27 of them. What fraction of her free throws did Tessa make? 3 18. A carousel has 56 horses. __ of them are white. How 8 many horses are not white? 19. Nathan works at a hardware store. Today he sold 5 of the tools he sold were hammers. How 48 tools. __ 6 many hammers did Nathan sell today? UNIT 3 LESSON 2 Multiplication with Non-Unit Fractions 49 Name 3-2 Date Complete each exercise about the pairs of fraction bars. 1. What equivalent fractions are shown? 2. Identify the multiplier. 3. What equivalent fractions are shown? 4. Identify the divisor. Write each amount as a decimal number. 84 5. _____ 31564 6. _____ 1,000 1,000 1176 7. ____ 100 876 8. _____ 1,000 Solve. Write a multiplication equation for each problem. Jonas has 8 sponsors for the school walk-a-thon. Maura has 3 times as many sponsors as Jonas. 1 as many sponsors as Jonas. Trenton has __ 4 9. How many sponsors does Maura have? Write the equation. 10. How many sponsors does Trenton have? Write the equation. 50 UNIT 3 LESSON 2 © Houghton Mifflin Harcourt Publishing Company 11. Stretch Your Thinking Hannah and Jo are driving separately to a restaurant that is 60 miles away 3 of the distance from their town. Hannah drives __ 5 5 __ and Jo drives of the distance before stopping for 6 gasoline. Who has driven farther? How many more miles does each driver need to drive to reach the restaurant? Multiplication with Non-Unit Fractions Name 3-3 Date The campers in each cabin at Bear Claw Camp held a contest to see who could walk the farthest in one day. Use the sign to answer the questions. Write your answers as fractions. 1 of the way to Otter 1. The campers in Cabin A walked __ 4 Ridge. How many miles did they walk? 2 2. The campers in Cabin B walked __ of the way to Silver 3 Stream. How many miles did they walk? 3 3. The campers in Cabin C walked __ of the way to Fossil Cave. 5 How many miles did they walk? 1 4. The campers in Cabin D walked __ of the way to Mammoth 6 Mountain. How many miles did they walk? 5. Which group of campers walked the farthest that day? 2 6. Show __ of 4 on the number line. © Houghton Mifflin Harcourt Publishing Company 3 0 1 2 3 4 2 7. Write __ of 4 as a fraction. 3 2 8. Write __ of 4 as a mixed number. 3 Multiply. Write your answers as fractions. 2 ⋅4= 9. __ 2 10. __ ⋅8= 5 11. __ ⋅4= 2 12. __ ⋅ 20 = 7 13. __ ⋅2= 3 14. __ ⋅5= 2 15. __ ⋅ 13 = 5 16. ___ ⋅ 18 = 5 17. __ ⋅ 12 = 7 9 3 UNIT 3 LESSON 3 3 9 12 6 8 9 Multiplication with Fractional Solutions 51 Name 3-3 Date Compare. 5 1. __ 5 __ 1 2. __ 1 __ 8 3. ___ 6 __ 6 4. __ 7 __ 2 5. __ 3 __ 8 6. __ 6 __ 6 7 7 5 8 3 4 10 4 9 8 7 Compare. 7. 0.54 0.65 10. 0.76 0.67 8. 0.207 11. 0.22 0.342 0.41 9. 0.5 0.47 12. 0.6 0.06 Multiply. 4 ⋅ 20 = 13. __ 2 ⋅ 14. __ 21 = 5 ⋅ 15. __ 24 = 1 ⋅ 16. __ 36 = 3 ⋅ 17. __ 16 = 2 ⋅ 18. __ 14 = 3 ⋅ 19. ___ 24 = 8 ⋅ 20. ___ 80 = 3 ⋅ 21. __ 45 = 5 3 8 4 9 10 9 22. Stretch Your Thinking Write a multiplication equation using one whole number and one fraction that have 18 . a product of ___ 8 52 UNIT 3 LESSON 3 Multiplication with Fractional Solutions © Houghton Mifflin Harcourt Publishing Company 12 7 Name 3-4 Date 3 __ Tanith is using a number line to find __ ⋅ 2 . This is her work so far: 4 5 0 1 – 5 2 – 5 3 – 5 4 – 5 1 0 1 – 5 2 – 5 3 – 5 4 – 5 1 0 — 20 1 — 20 2 — 20 3 — 20 4 — 20 5 — 20 6 — 20 7 — 20 8 — 20 9 — 20 10 — 20 11 — 20 12 — 20 13 — 20 14 — 20 15 — 20 16 — 20 17 — 20 18 — 20 19 — 20 20 — 20 1. Explain Tanith’s work so far to someone at home. 3 of each 2. Finish Tanith’s work by circling __ 4 circled fifth. How many 20ths did you circle altogether? 3 __ What is __ ⋅ 2? 4 5 2 __ 3. Use the number line to find __ ⋅ 5. 3 6 Label all the parts above and below. 0 1 Show your work. © Houghton Mifflin Harcourt Publishing Company Solve. 3 of a bag of popcorn. 4. Four friends at a party popped __ 4 They ate half of what was popped. What fraction of the popcorn in the bag did they eat? 7 5. Ashley brought __ gallon of lemonade to the party. 8 2 of it. How many gallons of Her friends drank __ 3 lemonade did they drink? Multiply. You do not need to simplify. 2 __ ⋅1= 6. __ 7 3 2 9. __ ⋅ 12 = 7 9 __ 12. ___ ⋅1= 10 2 UNIT 3 LESSON 4 4 __ 7. __ ⋅2= 1 __ 8. __ ⋅5= 4 __ 10. __ ⋅2= 1 __ 11. __ ⋅3= 5 13. ___ ⋅3= 5 __ 14. __ ⋅1= 9 5 12 9 3 8 7 6 6 5 6 Multiply a Fraction by a Fraction 53 Name 3-4 Date Name the mixed number shown by the shaded parts. 1. 2. 3. Add. 4. 454 + 0.65 = 5. 80.55 + 0.91= 6. 31.78 m + 6.2 m = 1 7. Show __ of 7 on the number line. 3 0 1 2 3 4 5 6 7 1 of 7 as a fraction. 8. Write __ 3 © Houghton Mifflin Harcourt Publishing Company 1 9. Write __ of 7 as a mixed number. 3 10. Stretch Your Thinking Solve for the unknown fraction. Then divide and shade an area model to show the 2 ⋅ = ___ ? 10 . equation. __ 5 54 UNIT 3 LESSON 4 30 Multiply a Fraction by a Fraction Name 3-5 Date Multiply. Simplify first if you can. 2 __ 1. __ ⋅6= 4 __ 2. __ ⋅1= 5 ___ 3. ___ ⋅ 8 = 2 __ 4. ___ ⋅8= 3 ___ 5. __ ⋅ 12 = 5 __ 6. __ ⋅3= 3 ⋅ __ 2 = 7. ___ 5 ___ 8. ___ ⋅ 2 = 5 24 4 10 7 9 15 17 7 25 3 8 25 5 __ 10. __ ⋅7= 12 6 7 ___ 11. __ ⋅ 6 = 9 1 16 4 ___ 9. ___ ⋅ 7 = 35 8 1 7 __ 12. __ ⋅2= 49 8 3 13. Which fraction is not equivalent to the others? 3 ___ 15 2 ___ 10 1 __ 5 9 ___ 45 10 ___ 50 6 ___ 40 7 ___ 35 100 ____ 500 Solve. Show your work © Houghton Mifflin Harcourt Publishing Company 3 of the animals are birds. Of the 14. In the town zoo, ___ 28 4 ___ are birds of prey. What fraction of the birds, 15 animals at the zoo are birds of prey? 5 15. Tuesday at the zoo, ___ of the visitors were adults. Of these 12 3 ___ were men. What fraction of the people who adults, 10 visited the zoo on Tuesday were men? 14 16. On Tuesday, ___ of the souvenirs purchased at the zoo gift 25 shop were stuffed animals. Of the stuffed animals purchased, 10 ___ were bears. What fraction of the souvenirs purchased at 21 the zoo gift shop on Tuesday were stuffed bears? UNIT 3 LESSON 5 Multiplication Strategies 55 Name 3-5 Date Add or subtract. 4 + __ 1. 1__ 52 1 + __ 2. 5__ 35 2 - __ 1 3. 1__ 3 + __ 5 4. __ 8 - __ 35 5. 7__ 1 6. 6 - 4__ 8. 132.76 - 87.24 = 9. 968.29 - 217.5 = 5 4 5 6 4 9 6 9 3 3 2 Subtract. 7. 31,763 - 6.51 = 3 __ 10. Use the number line to find __ ⋅ 2 . Label all the parts 4 5 above and below. 3 __ 4 ⋅ __25 = 0 1 © Houghton Mifflin Harcourt Publishing Company 11. Stretch Your Thinking Write a word problem that will 2 ___ ⋅ 8 = x in order to solve. Then use the equation __ 6 10 simplify and multiply to solve. 56 UNIT 3 LESSON 5 Multiplication Strategies Name 3-6 Date Find each product by first rewriting each mixed number as a fraction. 3 ⋅ 2__1 = 1. __ 7 2. 1___ ⋅5= 2 3. 2__ ⋅ 4__1 = 1 __ 4. 5__ ⋅3= 5 5. __ ⋅ 1__2 = 3 = 6. 12 ⋅ 2__ 1 7. 3__ ⋅ 3__1 = 9 = 1 8. __ ⋅ 3___ 7 2 5 3 5 9 2 2 10 3 8 4 9 10 Solve. Show your work. © Houghton Mifflin Harcourt Publishing Company 9. The bottom of Zeyda’s jewelry box is a rectangle with 3 1 inches and width 3__ inches. What is the area length 5__ 4 8 of the bottom of the jewelry box? 10. The Patel family went apple picking. The number of 2 times the number of red apples they picked was 2__ 9 green apples they picked. If they picked 45 green apples, how many red apples did they pick? 1 11. The art museum is 8__ miles from Alison’s house. 2 2 of the way there so far. Alison has ridden her bike __ 3 How far has she gone? UNIT 3 LESSON 6 Multiply Mixed Numbers 57 Name 3-6 Date Add. 3 + __ 1 1. __ 3 1 + __ 2. __ 5 + __ 1 3. __ 1 + __ 2 4. __ 2 + __ 1 5. __ 4 + ___ 1 6. __ 8 5 6 7 3 3 4 9 6 8 5 10 Use the Commutative Property to solve for n. 7. 55,207 + 87,331 = 87,331 + n n= 8. 48.76 + 20.08 = 20.08 + n n= Multiply. Simplify first if you can. 2 __ ⋅3= 9. __ 7 __ 10. ___ ⋅6= 3 __ 11. __ ⋅5= 5 ___ ⋅ 12 = 12. __ 1 __ ⋅4= 13. __ 2 __ 14. __ ⋅3= 4 3 25 2 7 7 5 9 6 8 15. Stretch Your Thinking Complete the mixed number equation that is represented by the area model. 1 __ 2 58 ⋅ = UNIT 3 LESSON 6 Multiply Mixed Numbers © Houghton Mifflin Harcourt Publishing Company 6 10 Name 3-7 Date Solve. 3 __ ⋅1 1. __ 2 - __ 1 2. __ 1 + __ 1 3. ___ 2 4. __ ⋅ 12 1 + __ 2 5. __ 3 1 + __ 6. __ 5 __ 7. __ ⋅5 11 + 8. ___ 3 4 - __ 2 9. __ 4 3 8 7 7 10 4 3 12 6 9 8 8 5 8 9 1 12. 10 - __ 7 __ 11. __ ⋅3 1 __ 10. __ ⋅1 3 5 9 9 4 Show your work. Solve. 7 gallon of water. It is 13. Rodrigo’s fish bowl holds __ 8 1 now __ full. How much water is in it? 2 © Houghton Mifflin Harcourt Publishing Company 1 14. Kenya jumped 7__ feet. Janet jumped 6 How much farther did Kenya jump? 1 6__ feet. 3 7 15. A group of hikers walked 8___ miles to Caribou Cave 10 1 __ and then 5 miles to Silver Stream. How far did they 5 walk altogether? 3 16. A recipe calls for __ cup of flour. Estevan wants to make 4 1 __ of the recipe. How much flour will he need? 3 1 17. A truck was carrying 2__ tons of sand. When it arrived, 8 1 only 1__ tons of sand were left. How much sand was 2 lost along the way? UNIT 3 LESSON 7 Relate Fraction Operations 59 Name 3-7 Date Subtract. 3 - __ 1 1. __ 2 - ___ 1 2. __ 7 - __ 1 3. __ 6 - __ 1 4. __ 4 - __ 2 5. __ 1 - __ 1 6. __ 4 6 7 9 5 3 10 3 8 2 4 8 Estimate each sum or difference. 7. 6.759 + 2.099 8. $44.25 - $21.76 9. 14.6 + 2.4 Find each product by first rewriting each mixed number as a fraction. 5 ⋅ 3__1 = 10. __ 8 3 3 11. 4__ ⋅5= 5 2 12. 1__ ⋅ 3__4 = 5 9 © Houghton Mifflin Harcourt Publishing Company 1 __ 13. 6__ ⋅5= 5 8 14. Stretch Your Thinking Give an example that shows how to use the Distributive Property to multiply a number by a sum. All of the numbers you use should be mixed numbers or fractions. 60 UNIT 3 LESSON 7 Relate Fraction Operations Name 3-8 Date Complete each fraction box. 1. 3 7 __ and __ > 8 3 6 7 > __ 7 > __ __ or __ 4 8 8 8 2. 3 1 __ and __ 2 4 5 > + + - - ⋅ ⋅ Show your work. Solve. 7 ton of 3. The Eagle Trucking Company must deliver __ 8 5 __ cement blocks and ton of bricks to one place. 8 How much will this load weigh? © Houghton Mifflin Harcourt Publishing Company 1 1 4. A truck carried 3__ tons of sand, but lost __ ton along 4 3 the way. How many tons of sand were delivered? 2 5. The trucking company also needs to deliver 1__ tons of 3 7 ___ oak logs and 1 tons of maple logs. Which load 12 weighs more? 3 1 6. In a load of __ ton of steel rods, __ of them are bent. 4 8 How many tons of steel rods are bent? 3 7. The company delivered 1__ tons of bricks to one building site. 5 1 __ They delivered 2 times this much to a second site. What was 2 the weight of the load the company delivered to the second site? UNIT 3 LESSON 8 Solve Real World Problems 61 Name 3-8 Date Multiply. 1. 2,548 × __5 2. 21 × 45 _ 3. 3,015 × __6 4. 33 × _4 5. 65 × 87 _ 6. 215 × __9 Find each product by first rewriting each mixed number as a fraction. 4 7. 4__ ⋅ 2__2 = 9 1 8. 6__ ⋅ 10 = 5 3 5 ___ 9. 3__ ⋅ 12 = 6 1 __ 10. 5__ ⋅3= 13 3 5 Solve. 6 - __ 2 11. __ 4 + __ 2 12. __ 3 2 ___ 13. __ ⋅ 9 3 __ ⋅5 14. __ 1 15. 8 - __ 3 1 + __ 16. __ 7 5 7 8 9 7 3 6 10 8 © Houghton Mifflin Harcourt Publishing Company 17. Stretch Your Thinking Write and solve a word problem that requires multiplying two mixed numbers. 62 UNIT 3 LESSON 8 Solve Real World Problems Name 3-9 Date Predict whether the product will be greater than, less than, or equal to the second factor. Then compute the product. 4 1. __ ⋅6=x 9 Predict: x 6 Compute: x = Predict: x 10 6 Compute: x = 2 __ 4. __ ⋅5=x 2 10 3. ___ ⋅6=x 1 2. 1__ ⋅6=x 5 6 5 __ Predict: x 6 Compute: x = 1 __ 6. 1__ ⋅5=x 6 Predict: x 6 Compute: x = 5 __ 5. __ ⋅5=x 6 Predict: x 3 5 __ 6 Compute: x = 6 Predict: x 5 __ 6 Compute: x = Show your work. Solve. 3 times as tall as his brother. His brother 7. James is 1__ 7 1 __ is 3 feet tall. 2 1 feet? Is James’s height more or less than 3__ © Houghton Mifflin Harcourt Publishing Company 2 How tall is James? 8. South Middle School has 750 students. North Middle 13 times as many students as South. School has ___ 15 Does North Middle School have more or fewer than 750 students? How many students attend North Middle School? UNIT 3 LESSON 9 Make Generalizations 63 Name Date Perry measured the foot length of four friends for a science fair experiment. Then, he made a bar graph to display his results. Foot Length Foot length (in.) 1. How much longer is Brennen’s foot than Clara’s foot? 2. What is the difference between the longest foot and the shortest foot? 9 8.8 8.6 8.4 8.2 8 7.8 7.6 7.4 Ch n Br en Cl ey ne a ar ne Ty e 0 en 3-9 Student Name Solve. 7 __ 3. __ ⋅4 3 4. 11 - __ 4 + ___ 7 5. __ 9 - ___ 5 6. ___ 7 + __ 2 7. ___ 5 ___ ⋅ 9 8. __ 8 12 4 9 15 12 5 3 6 10 11 Complete each fraction box. 5 7 ___ and __ 12 4 2 __ and __ 6 5 > + + − − ⋅ ⋅ © Houghton Mifflin Harcourt Publishing Company > 3 9. Stretch Your Thinking Write two multiplication equations using fractions and mixed numbers. Write one equation that will have a product greater than the first factor. Then write another equation that will have a product less than the first factor. 64 UNIT 3 LESSON 9 Making Generalizations Name 3-10 Date Divide 1. 5 ÷ 6 = 1 = 2. 9 ÷ __ 3. 33 ÷ 30 = 1 = 4. 8 ÷ __ 5. 3 ÷ 10 = 1 = 6. 4 ÷ __ 1 = 7. 100 ÷ __ 8. 1 ÷ 100 = 6 1 ÷ = 9. __ 8 5 1 ÷ = 11. __ 9 2 5 6 9 1 ÷ = 10. __ 7 8 1 ÷ = 12. __ 5 3 Show your work. Solve. 13. Alexander is dividing oranges into eighths. He has 5 oranges. How many eighths will he have? © Houghton Mifflin Harcourt Publishing Company 14. Carrie has 32 ounces of ice cream to divide equally among 10 people. How much ice cream will each person get? 15. Nayati wants to swim 50 miles this school year. She plans to 1 mile each day. How many days will it take her to swim __ 4 swim 50 miles? 1 16. Eric has __ of a watermelon to share equally with 3 friends. 3 How much will each person get? 17. A gardener needs to pack 16 pounds of beans into 20 bags. He wants all the bags to weigh about the same. About how much will each bag weigh? UNIT 3 LESSON 10 When Dividing Is Also Multiplying 65 Name 3-10 Add or subtract. 3 1. 2__ 2. 4 5 - 1__ _8 4. Date 7 5. 1 - 2__ _6 2 4__ 1 3. 10__ 2 3__ 6. 3 5 + 1__ _9 5 5 + 4__ _6 Complete each fraction box. 7. 2 2 __ and __ 5 2 4 - 3__ _5 8. 1 8__ 3 3 + 1__ _4 5 6 __ and __ 7 6 7 > > + + − − ⋅ ⋅ Predict whether the product will be greater than, less than, or equal to the second factor. Then compute the product. 3 10. __ ⋅5=x 2 ⋅5=x 9. __ 3 Compute: x = 5 Predict: x 6 Predict: x 5 Compute: x = 5 Compute: x = 12. Stretch Your Thinking Draw a diagram to show how many twelfths there are in 3. Describe a situation in which you would need to know how many twelfths there are in 3. 66 UNIT 3 LESSON 10 When Dividing Is Also Multiplying © Houghton Mifflin Harcourt Publishing Company Predict: x 1 11. 1__ ⋅5=x 3 3-11 Name Date 1 ÷ 1. Consider the division problem __ 3. 2 Describe a situation this division could represent. Draw a diagram to represent the division. Then find the solution. Write an equation. Then solve. Show your work. 2. A rectangle has an area of 12 square feet and a length of 5 feet. What is its width? 1 3. A tortoise must walk ___ mile to visit a friend. He plans to 12 break the journey into four equal parts with breaks in between. How long will each part of his journey be? © Houghton Mifflin Harcourt Publishing Company 1 4. Harry worked 7 hours last week. This is __ as many hours as 3 Aidan worked. How many hours did Aidan work? 5. Lin is a camp counselor. She is making small bags of trail mix for campers to take on a hike. She has 2 pounds of raisins and 1 pound in each bag. How many bags can she fill is putting __ 8 before she runs out of raisins? 1 6. Mr. Ramirez bought __ pounds of cashews. He divided the 4 cashews equally among his three children. How much did each child get? UNIT 3 LESSON 11 Solve Division Problems 67 Name 3-11 Date Add or subtract. 1. 4. 1 1__ 2. 2 5__ 5. 8 2 + 4__ _3 7 11 + 5___ 14 __ 1 6__ 3. 4 6. 4 5 – 4__ _6 2 – 2__ _5 1 9__ 3 8 + 7__ _9 5 6__ 8 1 + 3__ _2 Predict whether the product will be greater than, less than, or equal to the second factor. Then compute the product. 5 ⋅9=x 7. __ Predict: x 9 9 6 4 __ 5 Compute: x = 9 2 __ 12. __ ⋅4=x 5 Predict: x Predict: x Compute: x = 6 __ 11. __ ⋅4=x 5 Compute: x = Predict: x Compute: x = 1 __ 10. 1__ ⋅4=x Predict: x 5 8 Compute: x = 2 3 9. 1__ ⋅9=x 7 8. __ ⋅9=x 5 5 4 __ 5 5 Predict: x 4 __ 5 Compute: x = Divide. 14. 2 ÷ 3 = 15. 10 ÷ 3 = 1 = 16. 200 ÷ __ 1 ÷ = 17. __ 8 1 ÷ = 18. __ 6 4 4 4 7 19. Stretch Your Thinking Harrison is playing a board game that 1 of the has a path of 100 spaces. After his first turn, he is __ 5 1 fewer way along the spaces. On his second turn, he moves __ 4 spaces than he moved on his first turn. On his third turn, he 1 times as many spaces than he moved on his first moves 1__ 4 turn. What space is he on after three turns? 68 UNIT 3 LESSON 11 Solve Division Problems © Houghton Mifflin Harcourt Publishing Company 1 = 13. 6 ÷ __ Name 3-12 Date Solve. 1 = 1. 5 ⋅ __ 1 = 2. 5 ÷ __ 1 ÷ = 3. __ 2 4. 27 ÷ 10 = 1 = 5. 5 ÷ ____ 1 = 6. 12 ⋅ __ 3 ___ 7. __ ⋅ 10 = 1 = 8. 16 ÷ __ 3 8 100 5 27 1 ÷ 9. __ 10 = 5 1 11. __ ⋅ 14 = 8 3 9 4 1 = 10. 10 ÷ __ 5 12. 18 ÷ 20 = Tell whether you need to multiply or divide. Then solve. Show your work. 1 ounce. Jody has 1 pound 13. A dime weighs about ___ 12 (16 ounces) of dimes. About many dimes does she have? © Houghton Mifflin Harcourt Publishing Company 1 14. Maddie has 180 coins. Of these coins, ___ are dimes. 12 About how many dimes does she have? 1 15. A rectangle has length 3 feet and width __ foot. What is the 4 area of the rectangle? 1 16. A rectangle has area 3 square feet and width __ foot. 2 What is the length of the rectangle? 17. Nisha wants to study 5 hours for the spelling bee. If she 1 hour per night, how many nights will she studies __ 3 have to study? UNIT 3 LESSON 12 Distinguishing Multiplication from Division 69 3-12 Name Date Multiply. 1. 134 ⋅ 5 = 2. 44 ⋅ 21 = 3. 7 ⋅ 57 = 4. 4,507 ⋅ 3 = 5. 36 ⋅ 76 = 6. 1,928 ⋅ 6 = 1 = 8. 100 ÷ __ 1 ÷ = 9. __ 4 Divide. 1 ÷ = 7. __ 2 9 10. 4 ÷ 5 = 3 11. 12 ÷ 5 = 5 1 = 12. 8 ÷ __ 7 Show your work. Write an equation. Then solve. 13. Marc is running 5 kilometers at track practice. He decides to break the run into 3 equal lengths. How long will each length be? 70 UNIT 3 LESSON 12 Distinguishing Multiplication from Division © Houghton Mifflin Harcourt Publishing Company 14. Stretch Your Thinking Using a whole number and a fraction as factors, write a multiplication equation with a product less than the whole number factor. Draw a picture to show how the product is less than the whole number factor. Name 3-13 Date Show your work. Solve. 1. Dan’s Ice Cream comes in cartons of two sizes. The large 3 1 pounds. The small carton holds 1__ pounds carton holds 4__ 4 2 less. How much ice cream does the small carton hold? 2. Mac picked four baskets of blueberries. The weights of the berries in pounds are given below. Order the weights from lightest to heaviest. 5 __ 9 ___ 4 10 13 ___ 4 __ 5 20 1 3. Four cones of Dan’s Ice Cream hold __ pound. How much 2 ice cream does each cone hold? 1 4. If a dish of ice cream holds __ pound, how many dishes can 4 1 __ you get from a 4 -pound carton of Dan’s Ice Cream? 2 © Houghton Mifflin Harcourt Publishing Company Solve. Give your answer in simplest form. 1 = 5. 3 ÷ __ 3 + ___ 11 = 6. 1__ 9 7. ___ ⋅ 2__1 = 3 8. 2__ ⋅6= 5 14 3 4 16 5 3 = 1 + __ 9. __ 5 + __ 8 = 10. __ 1 ÷ = 11. __ 4 2 - ___ 1 = 12. __ 5 - __ 13. 3__ 11 = 7 __ 14. __ ⋅2= 5 3 8 7 2 UNIT 3 LESSON 13 6 5 8 9 10 7 Review Operations with Fractions 71 Name 3-13 Date 1 Use benchmarks of 0, __ , and 1 to estimate the sum or 2 difference. Then find the actual sum or difference. 5 + __ 4 1. ___ 10 13 – __ 3 2. ___ 14 9 7 Estimate: Estimate: Sum: Difference: 8 – __ 7 3. __ 9 13 + __ 3 4. ___ 14 8 4 Estimate: Estimate: Difference: Sum: Show your work. Write an equation. Then solve. 5. A rectangle has an area of 20 square feet and a length of 6 feet. What is its width? 6. Bailey attends gymnastics practice for 8 hours each week. 1 the number of hours that the gym is open for This is __ 4 practice. How many hours is the gym open for practice? Solve. 1 8. __ ⋅3= 1 ÷ = 7. __ 3 4 4 1 = 9. 14 ⋅ __ 6 © Houghton Mifflin Harcourt Publishing Company 1 ÷ 5 different 10. Stretch Your Thinking How is solving __ 8 1 from solving __ ⋅ 5? 8 72 UNIT 3 LESSON 13 Review Operations with Fractions Name 3-14 Date These graphs show the instruments in two different high school marching bands. Carter School Marching Band 1 – 3 percussion Reagan School Marching Band 2 – 5 brass 1 – 3 1 – 6 percussion woodwind 1 – 2 brass 4 — 15 woodwind Show your work. Solve. Use the circle graphs. 1. The Reagan School Marching Band has three percussion musicians. How many musicians altogether are in the band? © Houghton Mifflin Harcourt Publishing Company 2. There are 30 musicians in the Carter School Marching Band. How many of them play brass instruments? Suppose both bands decide to combine and perform as one band. 3. What fraction of the band members will play a brass instrument? 4. What fraction of the band members will play a percussion instrument? 5. What fraction of the band members will play a woodwind instrument? UNIT 3 LESSON 14 Focus on Mathematical Practices 73 Name 3-14 Date Show your work. Solve. Explain how you know your answer is reasonable. 1 feet and a width 1. James’s garden has a length of 12__ 4 2 of 9__ feet. What length of fencing will he need to 3 surround his garden? Answer: Why is the answer reasonable? Solve. 1 ÷ = 2. ___ 3 1 = 3. 6 ÷ __ 2 __ 4. __ ⋅5= 1 ÷ = 5. ___ 5 1 = 6. 7 ⋅ __ 1 7. __ ⋅ 12 = 11 3 12 8 3 7 5 Show your work. Solve. 1 pound altogether. What 8. Kayla packs 4 boxes that weigh __ 6 does each box weigh? © Houghton Mifflin Harcourt Publishing Company 2 9. Mrs. Blackwell put 4__ grams on the scale during a lab in 3 5 grams to the scale. How science class. Then, she added 2__ 6 many grams are on the scale in all? 10. Stretch Your Thinking If you start with 1 and repeatedly 1 , will you reach 0? Explain why or why not. multiply by __ 2 74 UNIT 3 LESSON 14 Focus on Mathematical Practices